1-s2.0-001379448790035X-main

Engmeering Fraclure Mechanics Vol. 26, No. 6;pp. 869-882, 1987 0013-7944/87 $3.00 + .I0 Printed in Great Bntain. 0 1987 Perzqmm Journals Ltd.

FATIGUE THRESHOLD DETERMINATION IN HIGH STRENGTH COLD DRAWN EUTECTOID STEEL WIRES

J. LLORCA and V. SANCHEZ-GALVEZ Department of Materials Science, Universidad Polittcnica de Madrid, Ciudad Universitaria,

Madrid 28040, Spain

Abstract-The effect of stress ratio on fatigue threshold in cold drawn eutectoid steel wires has been experimentally measured. Crack growth rate measurements in the threshold region have been accurately determined using SEM. These results are compared with others from literature showing that fatigue threshold decreases when yield strength increases in pearlitic steels.

1. INTRODUCTION

THE EXCEPTIONAL mechanical properties of the cold drawn eutectoid pearlitic steels have permitted its utilization in big civil engineering structures, such as long span prestressed concrete bridges or nuclear power plants. In many cases, the most severe conditions of design loading are cyclic, and this fact has given impulse to study of the fatigue behaviour and particularly the fatigue limit of these steels.

Among the studies performed to determine the fatigue limit of these materials, the work done by FernLndez and others[2,7] must be pointed out. This study, involving a high level of experimental work, shows that the classical design method based upon Wiihler curves is not directly applicable without the support of statistical models due to the high scatter of the empirical results (Fig. 1). The reason for such a high scatter must be found in the surface state of these steels and fracture mechanics is the only way to achieve results used in engineering design.

On the other hand these steels show low fatigue properties as compared with their mechanical properties under monotonic loading, like the high strength martensitic steels. Usually, the fatigue limit 0, for a stress ratio R = 0 is similar to the cyclic yield stress o&3]. For mild steels o,,~= 0.65 or and thus +/o,zO.65. This condition is equivalent to the assumption that plastic strains must develop in a smooth surface to initiate a crack. Previously[4], the authors have obtained

390

-!- f... ..._... t 380

-C

5 370 1

. . . ._m . . . . . . .

. . ..__.. . . . . .

. ..a__.. _ . .

. FAILURE O-RUN OUT

4 360

t

. .... . . . . . S... . . . . . . . . . ... . . . . .

350- . . . . . . . . . . . . . . .

% . . . . . . . . . -.._ . .

5 340- . . . .- . .._ . . . . . . . .

L2: . . . . . . . . . . . . . . . . .

330- . . . . . . . . . . . . . f . . . . .

?I . . . . . . . . . . . . . . . . . . . .

k! 320- . . . . . .._.. . . . . ._.. . . .

z . . . . . I. . . . . _ . . . . . . .

310- . . . . . . . . . . . . . . . . . . . .

. .*. . . . . . . . . . . .

3OG- . . . . . . . . 1

. . . . . 1

290- . . 2 .

2.30 2

1 I 1 1 1 2

5.104 105 2.105 5.105 106 2.106 5.106

20-

NUMBER OF TESTS

20

20

20

20

20

20

20

20

20

20

20

20

20

24

- 24

- 24

- 24

- 24

- 24

- 24

- 24

- 24

CYCLES Fig. 1. Experimental evidence of the large scatter in fatigue life of eutectoid cold drawn wires (from

reference [Z]).

870 J. LLORCA and V. SANCHEZ-GALVEZ

experimentally the cyclic yield stress in cold drawn eutectoid steel wires. Tests were performed on smooth specimens under strain control and strain ratios R,= E,in/Emax >O. When &,,, 0.55% cyclic softening was observed, which increases with smax and As. For instance, for &iX = A&, the oYc is equal to 0.92 oY.

In accordance with that, a high fatigue limit for these steels could be expected. However, it is well known that those high values are never achieved. Since fifty years ago, Pomp and Duckwitz[5] found that the fatigue limit of cold drawn steels decreased with the increase of reduction of area during the drawing process and it was in between 40% of the ultimate tensile strength for a reduction of area of 44% and 25% of the u.t.s. for a reduction of 90%.

Castillo[2] performed 72 tests with specimen lengths ranging from 140 to 8540 mm. His results show a fatigue limit between 0.2 and 0.3 oY depending on the specimen length. Birkenmaier and Narayanan[6] performed more than 200 tests and found a relation or/c+ = 0.23 for specimens of 200 mm of length. Similar values were found by Verpoest and others[7] testing 2 mm diameter wires and different values of the yield stress (see Table 1).

Such wide experimental results clearly indicate that high stress concentrations must exist on the surface of these steels, leading to low cyclic stresses to initiate a crack. These stress concentrations might be produced either by imperfections of the steel surface or by the interface between matrix and inclusions, which could possess different mechanical properties. Fowler[8] has shown the detrimental effect on the fatigue limit of the increase in the content of inclusions in eutectoid pearlitic steels. If the main cause of the low fatigue limit of cold drawn eutecoid steels were the inclusions, no differences would be observed when the steel surface was polished to eliminate surface imperfections. PO-we Kao and Byrne[27] carried out such work, but they found that a higher resistance to fatigue crack initiation is obtained when the specimen surface was polished in cold drawn steels. On the other hand, several authors[7,9] reported that crack propagation begins at the tip of a surface flaw (Fig. 2).

The surface state of these steels has been deeply examined by Cetial[lO]. Flaws found were inclusions, cavities and cracks associated to the cavities. The mean width of the inclusions (perpendicular to the wire axis) was measured. In the majority of the samples studied, cavities deeper than 50 pm were found, and associated to these cavities, cracks with lengths up to 40 urn were also found.

Verpoest and collaborators[7] assumed that, for these steels, cracks propagate from the very beginning from surface flaws, without any crack initiation time. According to the experimental results outlined above, this assumption can be checked: No fatigue crack initiation exists because cracks are always present on the steel surface. Therefore, no fatigue failure will happen provided that the stress intensity factor range AK is below the threshold value AKth. It follows the importance of the determination of the threshold stress intensity factor range AKth to characterize the fatigue behaviour of cold drawn eutectoid steels.

It is well known the large influence of the stress ratio R on the threshold stress intensity factor range AKth[l 11. This influence has a prime importance for a safe design with these steels, and it has been the main objective of this research.

Table 1. Experimental values of fatigue limit (oj) and yield strength (o,) for eutectoid cold drawn wires

Reference Number of Tests

Specimen length (mm)

(M%a)

32 140 1500 415 0.27 26 1960 1500 315 0.21 14 8540 1500 294 0.20

210 200 1548 360 0.23 35 1111 390 0.35 68 1207 366 0.30 38 1578 421 0.27 36 1902 471 0.25 35 1952 565 0.29

Threshold determination in eutectoid steel wires 871

Fig.

Fig. 2. Surface defect from which fatigue crack began to propagate (x 400).

Fig. 3. Fatigue crack coloured by heat treatment.

4. SEM Micrograph showing differences between crack propagation near threshold (left) and posterior fracture (right) ( x 550).


Fig. 10. Fatigue crack SEM with AK=20 MPa no;* showing a ductile fracture mechanism (x 2040).

Fig. 11. Fatigue crack SEM with AK=5 MPa # ( x 2040).


2. EXPERIMENTS

Material The chemical composition and the mechanical properties of the steel are summarized in Table

2. The processing of the steel included the production of 12 mm diameter wires by rolling. These wires were austenized at 1200C and patented in a lead bath at 850C and finally cooled in air; after which the wires were cold drawn in several passes until 7 mm diameter wires were achieved. The final product was stress-relieved by heating at about 450C for a few seconds. The microstructure is a fine pearlite with an interlaminar distance in the pearlite below 0.25 p.

Crack growth rate determination Due to the small diameter of the steel wires and its circular shape, the usual techniques used

to determine the crack growth rate are difficult to apply for obtaining the threshold stress intensity factor range, that involves a high accuracy in the measurements[12].

The travelling microscope yields very accurate measurements of the crack growth in the surface, but for the geometry under study, there is a state of plane stress in the surface, while in the inside of the specimen there is a state of plane strain. Numerical calculations provide accurate values of the stress intensity factor along the crack front inside the specimen, but fail to give a definite value in the surface, since there the degree of the singularity depends on the angle between the crack front and the surface of the specimen[13]. Therefore, although accurate values of the crack growth rate might be obtained, it would not be possible to derive a correlation with accurate values of the stress intensity factor range.

The technique based upon the measurement of the compliance of the specimen yields good results at high crack growth rates (above 10m9 m/cycle) but it is not appropriate for lower rates due to the high scatter of the results at the low values of the load necessary for obtaining the AL

Other systems more sophisticated (acoustic emission, holography or high frequency alternating currents) permit the detection of small cracks. For instance, with the use of alternating currents of 40 kHz of frequency, cracks with an area of about 0.05% of the total area of the wire can be detected. But the system fails to give accurate information about the depth of the crack, not uniquely related to the area of the crack. On the other hand, the electric noise introduces a scatter not negligible as compared with the low voltage drops measured[12]. Summarizing, although these techniques have permitted important advances in the detection and study of microcracks, its utilization for the obtention of the threshold stress intensity factor range for crack growth involves a high scatter of the results.

The method followed for the measurement of the crack depth increment Aa had the aim of achieving a high accuracy. With that aim, after fatigue precracking, the specimen was lightly heat tinted. In tests at R = 0.5 and R 2 0.8, the specimen was heated at 200C for about 15 minutes while in tests at R = 0.1 the heating time was reduced to 10 minutes. In this way, the oxide film was thinner and its possible influence on the threshold stress intensity factor range by crack closure was lessened. After testing, the specimens were fully broken in tension in air and the crack depth increment Aa was measured by means of a profile projector and a scanning electron microscope. The area of crack growth was easily distinguishable from the precrack by its different colour and from the final ductile fracture by its different texture (Figs 3 and 4). With this system an accuracy of f 3 pm in the measurement of Aa was achieved.

Experimental method Tests were performed on 7 mm diameter wires in an Instron dynamic testing machine under

load control and sinusoidal wave. The frequency was different from one test to another, but always below 20 Hz, since it is known that it has no influence on the crack growth[14]. Both in the Paris

Table 2. Chemical composition (X) and mechanical properties of steel tested

C Mn Si P S N (&a)

q.0. I %

Q2 WI (M>a) (2) (g

0.82 0.60 0.18 0.010 0.024 0.007 197.000 1340 1370 1720 5.06 29.6


range (da/dN > lo- m/cycle) as well as in the range near the threshold the crack growth rates were determined.

In the Paris range, specimens were previously notched by means of a file, the notch depth being about 1 mm, and then fatigued at a constant load amplitude. The crack growth rate was obtained by measuring the stiffness change by means of a dynamic extensometer of 12.5 mm gauge length attached to the lips of the notch. A previous calibration curve of crack depth vs specimen stiffness gives the actual crack depth during the test.

In the tests performed to determine the threshold stress intensity factor range, a notch of straight front and 1.0 or 1.2mm of depth was previously produced by electro-erosion. It was checked that with this technique the loads needed to initiate a crack were lower than with notches produced by machining, probably because the former way induces lower compressive stresses in the notch tip than the machining way. With this method, the number of load blocks of decreasing amplitude required to arrive at the threshold is lower, easing the procedure.

In order to obtain reliable values of AKth, the crack closure effect had to be taken into account. To avoid that problem, cracking was produced following different systems for different values of R. For values of R 2 0.8, the maximum stress was held constant, and the minimum stress was progressively increased until AK was small enough (Fig. 5a). For R = 0.5, cracking was produced at R = 0 and then, the maximum stress was progressively reduced (Fig. 5b). For R =O.l, cracking was also produced at R = 0 and the maximum stress reduced for each stress block. In the last two blocks before reaching a AK value close to the threshold the maximum stress was reduced by only lo%, according to the usual techniques for this kind of test (Fig. 5~). During precracking, crack growth was tracked by means of a dynamic extensometer. In all tests, the crack propagated at least 200pm in the last loading block. This length is much greater than the plastic zone size that could be produced by any hazardous overload during the last loading blocks.

K T Rz0.5

R = 0.1

Fig. 5. Fatigue precracking scheme for (a) R > 0.8 tests, (b) R = 0.5 tests, (c) R = 0.1 tests


Table 3. Paris law parameters for different stress ratios

R c m (m/c x lo-) (Go)

0.8 4.633 1.993 96 0.5 2.052 2.293 98 0.1 1.107 2.417 98.3

After precracking, the specimen was heat tinted in the way described before and was subjected to the desired cycling loading. Finally, the specimen was broken under monotonic loading and the crack growth Aa in the center of the crack was measured.

From the values Ao and a, the stress intensity factor range AK was determined by the expression[ 141

AK = MAafia (1)

valid for a/D values greater than 0.15, the parameter M being

M = (0.473 - 3.286(a/D) + 14.797(a/D)2)2((a/D) - (a/D)2)-4 (2)

where D is the diameter of the wire.

3. RESULTS AND DISCUSSION

The experimental results obtained for the 3 values of R used, are shown in Fig. 6. As can be seen in all cases, a change of slope in the curve da/dN vs AK can be observed for da/dN about 10m9 m/cycle. For greater values, the material follows the Paris law and the values of the parameters A and m are shown in Table 3.

The three straight lines best fitting the results are drawn in Fig. 7. As can be seen, higher R values yield crack growth rates slightly greater for small AK values. This fact, reported previously by other authors[15] can be explained taking into account that the influence of crack closure increases when AK decreases. When AK increases, the three straight lines are nearly convergent. Anyhow, the difference is small and the scatter of the results does not permit us to get more information.

Figure 8a illustrates the results for the range near the threshold. Figures 8b and 8c show the scatter intervals of the experimental results of crack growth rates and stress intensity factor ranges taking into account the accuracy of measurements of Aa and loads.

These results have been used in the determination of AKth for the three R values following the criteria recently exposed by Taylor[16] in a review. He points out, after having analyzed more than seventy papers with experimental values of AKth, that some criteria need to be adopted to guarantee that a value is reliable. If the testing procedure is not appropriate, the threshold value may be overestimated by the existence of overloads or even underestimated if the cracks are small. The two main criteria proposed by Taylor are: first, that the da/dN vs AK curve must include at least one value below lo-lo m/cycle. When this condition is fulfilled and no clear asymptote parallel to the da/dN axis exists, the threshold stress intensity factor range AKth is the value corresponding to a crack growth rate of lo- m/cycle. According with these conditions, AK, values have been determined and they are summarized in Table 4.

Table 4. AKth for different stress ratios

R da/dN (m/c x 10.*I)

da/dN scatter (m/c x 10.~)

A& scatter

0.8 1.06 0.74-1.37 2.8 2.3-3.3 0.5 1.28 1.161.40 3.8 3.54.2 0.1 1.10 l.OG1.22 5.2 5.0-5.4


(a) lC6jC

2 ttT7 - i P :: xi3 -

tog-

(b)

0

0

R 2 0.8 da/dN = C iAKlm

C : 4.633 .lO-

m = 1.993

R 3 0.5

daidN : C (AK)

C = 2.052.16

m : 2.293

R.= 0.1

da/dN = C (AK)m

c = 1.107.,0 16 - 0 m : 2.417

r = 93.4%

-12 10 L I 8 I L ,

1 2 5 10 20 50 100

AK .(MPa.m2)

AK ,(MPa rn?

AK 1 (MPa m)

Fig. 6. (a) Crack growth rate vs AK for R 3 0.8, (b) for R = 0.5, (c) for R = 0.1.


- R zO.8

/ ---- R ~0.5

-..- .._ R ~0.1

15 25 50 100

AK (MPa.rn2) ,

200

Fig. 7. Comparison between region II crack growth rates for different R values.

The influence of R on the crack growth rate is greater near the threshold. The experimental results show that, for the steel tested, the crack propagation rate at AK=5 MPa ml/* is two orders of magnitude greater for R = 0.8 than for R = 0.1. Although qualitatively this phenomenon has been widely explained[ll], the efforts to give a quantitative explanation from a theoretical model have not been successful, due to the large influence of microstructural factors.

Actually, these factors may produce an increment of crack closure by increasing the roughness of the crack surface, or provide different preferential orientations for the advance of the crack front leading to crack branching. The influence of these microstructural factors is thus very important and not easily quantified. In pearlitic steels, the two main characteristics are the austenitic grain size and the interlamellar spacing of the pearlite[19]. Large austenitic grain sizes as well as high pearlite interlamellar distance produce rougher crack surfaces, increasing the crack closure effect and diminishing the effective force available to produce the crack propagation.

Among the empirical expressions proposed[17], [18], the simplest one that gives a good fit to experimental results has been the linear relationship[20], [21]:

AKlh = AKtho - AR. (3)

Figure 9 shows the best fit to the experimental results by a straight line for the three R values used, and a good agreement can be observed.

The value of the parameter A has to be a function of the mechanical properties and the microstructure of the steel. Since for pearlitic steels the yield stress is a function of the pearlitic interlamellar spacing, it can be assumed that the A value will decrease for stronger steels giving rise to a weaker influence of R on the threshold value. Table 5 includes a compilation of the existent bibliography for ferritic-pearlitic steels with a pearlitic content above 80%. With the exception of the results of Mausonave and Bailon, all the results are in agreement with this dependence of R with the yield stress.

Finally, another result can be discussed. Crack growth rates one order of magnitude lower than the interatomic distance (about 2.1O-O m) have been measured. This fact means that the actual crack propagation is discontinuous along the crack front, whilst for da/dN greater than about lo- m/cycle, the propagation curve follows the Paris law and the crack growth is continuous. At high growth rates the fracture topography is the typical one for fatigue of pearlitic steels (TTS)[28]. At low growth rates (below about 10m9 m/cycle) the fracture mechanism is different showing a faceted crack path [19] (see Figs 10 and 11).


(a) lo76

A l

A l

0 l

A

l

I-do

! .A

O l e

0

16 0 a A

0 RZ0.8 l R:0.5 A R-0.1

Id2 1

I I I I

1 2 5 10 20

z_ m 1@- z S! 8

c( WI

,-dJ- c( Y

nn

;bO- k +ii

w

16 - -- w

-

Iti I I I I 1 2 5 10 20

(4 167

#II 1 2 5 10 20

AK ,(MPo.m*)

AK, (MPa .rn*)

AK, (MPa.m"*)

Fig. 8. (a) Experimental results of crack growth rates in the near threshold region. (b) AK Experimental confidence limits. (c) da/dN Experimental confidence limits.


6- AKth=5.54-3.43R

1 I I I I 0.0 0.2 0.4 0.6 0.6

R

1.0

Fig. 9. AK,, experimental dependence with R.

4. THE INFLUENCE OF oY AND R ON AKTH

As it was outlined above, the AK,, depends on the mechanical and microstructural properties of the steel. In pearlitic steels, there exists a simple relationship between them, because the higher the yield stress, the lower the pearlite interlamellar distance. Therefore, it seems possible to estimate AKth from cry, and this possibility would be very interesting since the yield stress determination is quite simple. The results previously published have found such a relationship for martensitic steels[16], [20] but not for pearlitic steels. The reason for this failure could be the lack of data for high yield stresses, the necessity of comparing results for the same R value and the scatter of the empirical results. To avoid this last problem and achieve reliable data, the criteria outlined by Taylor[16] have been followed.

Figures 12 to 14 illustrate the AKth values as a function of aY with our data as well as data of the literature, for R = 0, R = 0.1, and R 2 0.6, and steels with pearlitic content above 80%. Despite a high scatter, there is a clear trend to decrease AKth when cry increases. These figures also show some phenomena that can be discussed.

First of all, the influence of cr,, on AK,, is less important for higher R values (see Fig. 14, for R 2 0.6) despite the few available results. The explanation might be as follows: The two main effects promoting the crack closure are the plasticity induced near the crack tip and the surface roughness; since for high R values the crack is always open and the CTOD values are greater than the crack rugosities, the only effect on the crack closure is the plasticity induced and thus the influence of R is much smaller.

On the other hand, for aY > 1200 MPa, a lower influence of R on AK,, is observed than for lower or values. This effect may be understood taking into account that high yield stresses give

Table 5. Influence of yield strength on A parameter

Reference Steel my (MPa) A

1211 WI WI ~231 Cl81 Cl81 Cl81

This Paper

ANC 480-540 5.64 ACN 47&507 6.76

P 434 7.24 M 337 11.84 6-2 477 11.44 6T 477 12.99

532 11.28 NE& 1370 3.43


DATA FROM REFERENCES :

[7] .[8]. [211 8 [4 0 [4 8 [26]

6-

I I I 1

0 400 800 1200 1600 260

Oy ,(MPa)

Fig. 12. AKth experimental values for pearlitic steels with R = 0.

rise to smaller plastic zones and to microstructures in which the roughness is lower. If the crack closure effect is lower, so will be the influence of R.

Finally, the straight line of Fig. 13 (R = 0.1) shows a higher slope than the line of Fig. 12 (R = 0), which is opposite that expected. Although the scatter of results for R = 0.1 is so high that no definitive conclusions can be derived, this anomalous behaviour may be attributed to the decrease of surface roughness in the tests at R = 0 by fretting and erosion between the two lips of the crack when it is fully closed in each cycle. The particles pulled out by this friction may fill up the valleys of the crack surface and the final result may be a smooth surface leading to a lower influence of the crack closure induced by the roughness (Fig. 15). This effect must be taken into account when A&, values were extrapolated from results obtained at different R values. because the AKtho value determined may be overestimated.

ru- >E

d

2. .c

=1

lo-

6-

DATA FROM REFERENCES:

0 400 800 1200 1600 2&o

Oy , (MPa

Fig. 13. AK,, experimental values for pearlitic steels with R = 0.1.


(1)

(2)

(3)

DATA FROM REFERENCES : [IS], [19] , [21] , 1221 , and this paper

6- R ~0.6

U,, , Wa)

Fig. 14. AK,,, experimental values for pearlitic steels with R 3 0.6.

5. CONCLUSIONS

For the first time, reliable values of AKth as a function of R have been determined for eutectoid cold drawn steels. Due to the existence of surface flaws and cracks in actual steel wires, the values obtained are of prime importance for fatigue design. The experimental method used for obtaining AKth values, although it is quite tiresome, has permitted the achievement of a high accuracy of the results. It has been checked that pearlitic steels also show a decrease of AKth when oY increases, if the results of the literature are rationalized as a function of R.

Acknowledgements-The authors are indebted to Comision Asesora de Investigacibn Cientifica y Tkcnica by the financial support for this research through grant number 1459/82.

Fig. 15. Scheme of roughness induced closure diminution when R = 0.


REFERENCES

[l] A.Fernandez, V. Esslinger and B. Thiirlimann, Ermiidungsfiestigkeit von Bewehrungs- und Spannstlhlen, Bericht NC. 8002-l. Institut fiir Baustatik und Konstruktion, Zurich (1984).

[2] E. Castillo, A. Fernandez, V. Esslinger and B. Thiirlimann, Statistical model for fatigue analysis of wires, strands and cables. Report 8002-2. Institut fur Baustatik und Konstruktion, Zurich (1983).

[33 K. J. Miller, Initiation and growth rates of short fatigue cracks, Fundamentals of Deformafion and Fracture (Edited by Bilby, Miller and Willis), pp. 477-500. Cambridge University Press(1985).

[4] J. LLorca and V. Sanchez Galvez, Condiciones para Iniciacion y Crecimiento de microfisuras en alambres de pretensado. An. Met. Fractura 2, 169-176 (1985).

[S] A. Pomp and C. A. Duckwitz, Daverpruf~ngen unter Wechselnden Zug~an-sprunchungun an Stahldraten, Mirfe~lungen aus dem Kaiser Wi~heim-insfilu~, 8 (1931).

[6] M. Birkenmaier and R. Narayanan, Fatigue resistance of large high tensile steel stay tendons, Fafigue of steel and concrete structures, Colloquium Lausanne, IABSE, 663-672 (1982).

[7] I. Verpoest, E. Aernoudt, A. Deruyttere and M. De Bondt, The fatigue threshold, surface conditions and fatigue limit of steel wire, Int. J. Fafigue 7, 199-214 (1985).

[8] G. J. Fowler, The influence of non-metallic inclusions on the threshold behaviour in fatigue. Mater. SC;. Engng 39, 121-126 (1979).

[9] J. LLorca and V. Sanchez Galvez, Consideraciones acerca de1 umbra1 de propagation de fisuras por fatiga en aceros perliticos. An. Met. Fracfura, in press.

[lo] F. J. Cetial, Caracterizacion metalogr~fica de1 estado suerficial de tendones de accro eutectoide para hormigon pretensado. Master Thesis, Universidad de Navarra, Espaiia.

[1 l] R. 0. Ritchie, Thresholds for fatigue crack propagation. Questions and anomalies. Adv. Fracture Res., 6th Int. Conf. Fracfure (pp. 2355259) Nueva Delhi, India (1984).

[12] I. Verpoest, E. Aernoudt, A. Deruyttere and M. Neyrinck, An improved AC potential drop method for detecting surface microcracks durina fatigue tests of unnotched specimens. Fafigue Engng Mafer. Sfructures 3, 203-217 (1981).

[13] M. A. Astiz, An incompatible crack tip singular elemeni to be used in-fracture mechanics. Int. J. Fracfure. Submitted for publication.

1147 A. Valiente, V. Sanchez-Gilvez and M. Eticcs, On fatigue cracking in prestressing steel wires. Adv. Fracture Res., 6fh Int. Co& Fracrure (pp. 2143.--2151), Nueva Delhi, India (1984).

[15] R. 0. Ritchie, Near-threshold fatigue crack propagation in ultra-high strength steel: Influence of load ratio and cyclic strength. J. Engng Maier. Teclmol. 99, 195-204 (1977).

[ 161 D. Taylor, An analysis of data of fatigue crack propagation thresholds. Proc. Fafigue 84 (pp. 3277337), Birmingham, U.K. (1984).

1171 M. Klesnil and P. Lukas, Effect of stress cycle assymetry on fatigue crack growth. Ma&r. Sci. Engng 9, 231-239 (1972).

[18] J. Mausonave and J. P. Bailon, The dependence of the threshold stress intensity factor on the cyclic stress ratio in fatigue of ferritic-pearlitic steels. Scripta Metall. 9, 723-730 (1975).

El91 G. T. Gray, J. C. Williams and A. W. Thompson, Roughness-induced crack closure: An explanation for m~crostructurally sensitive fatigue crack growth. Metali. Tram 14A, 421433 (1983).

[20] 0. Vosikovsky, The effect of stress ratio in fatigue crack growth rates in steels. Engng Fracfure Me&. 11, 595-602 (1979).

[21] J. M. Rodriguez, J. Gil and M. Fuentes, El umbra1 de fatiga en un acero ferritico-perlitico con 0.5% de C. Revtu Metal. 20, 21-25 (1984).

1221 C. J. Beevers, R. J. Cooke, J. F. Knott and R. 0. Ritchie, Some considerations of the inhuence of sub-critical cleavage growth during fatigue crack propagation in steels. Metal Sci. 9, 119-126 (1975).

[23] R. J. Cooke and C. J. Beevers, Slow fatigue crack propagation in pearlitic steels. Mater. Sci. Engng 13, 201-210 ( 1974).

[24] C. Naiiez and J. G. Byrne, Fatigue improvement of eutectoid steel by subcritical TMTs. Proc. Fatigue 84 (pp. 401- 410), Birmingham, U.K. (1984).

[25] K. Hambcrg and B. Karlsson, Crack propagation in eutectoid steel. Prof. Fatigue 84 (pp. 391400), Birmingham, U.K. (1984).

[26] R. J. Cooke and C. J. Beevers, The effect of load ratio on the stresses for fatigue crack growth in medium carbon steels. Engng Fracture Mech. 5, 1061-1071 (1973).

[27] PO-We Kao and J. Byrne, Fatigue initiation study of TMT eutectoid steel Mefall. Trans. 13A, 855-864 (1982). 1281 A. W. Thompson and J. C. Chestnut, Identification of a fracture mode: The tearing topography surface. Metall.

Trans. IOA, 1193-l I96 (1979).

(Received 4 Augusf 1986)

1-s2.0-001379448790035X-main

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